Puzzles of Dark Matter-More Light on Dark Atoms?

arXiv:1011.4587v1 [hep-ph] 20 Nov 2010

Puzzles of Dark Matter - More Light on Dark Atoms? Maxim Yu. Khlopov1,2,3 , Andrey G. Mayorov 1 , Evgeny Yu. Soldatov 1 1 National Research Nuclear University ”Moscow Engineering Physics Institute”, 115409 Moscow, Russia 2 Centre for Cosmoparticle Physics ”Cosmion” 115409 Moscow, Russia 3 APC laboratory 10, rue Alice Domon et L´ eonie Duquet 75205 Paris Cedex 13, France

Abstract Positive results of dark matter searches in experiments DAMA/NaI and DAMA/LIBRA confronted with results of other groups can imply nontrivial particle physics solutions for cosmological dark matter. Stable particles with charge -2, bound with primordial helium in O-helium ”atoms” (OHe), represent a specific nuclear-interacting form of dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct methods of underground Dark matter detection using its nuclear recoil. However, low energy binding of OHe with sodium nuclei can lead to annual variations of energy release from OHe radiative capture in the interval of energy 2-4 keV in DAMA/NaI and DAMA/LIBRA experiments. At nuclear parameters, reproducing DAMA results, the energy release predicted for detectors with chemical content other than NaI differ in the most cases from the one in DAMA detector. Moreover there is no bound systems of OHe with light and heavy nuclei, so that there is no radiative capture of OHe in detectors with xenon or helium content. Due to dipole Coulomb barrier, transitions to more energetic levels of Na+OHe system with much higher energy release are suppressed in the correspondence with the results of DAMA experiments. The proposed explanation inevitably leads to prediction of abundance of anomalous Na, corresponding to the signal, observed by DAMA.

1

Introduction

In our previous paper [1] we have shown that the set of conditions for dark matter candidates [2, 3, 4]can be satisfied for new stable charged particles, if they are hidden in neutral atom-like states. To avoid anomalous isotopes overproduction, stable particles with charge -1 (like tera-electrons [5, 6]) should be absent, so that stable negatively charged particles should have charge -2 only. In the row of possible models, predicting such particles [7, 8, 9, 10, 9, 11, 12, 13, 14] stable charged clusters u ¯5 u ¯5 u ¯5 of (anti)quarks u ¯5 of 5th family from the spin-charge-family-theory [15] can also find their place (see [16]). 1

In the asymmetric case, corresponding to excess of -2 charge species, they bind in ”dark atoms” with primordial 4 He as soon as it is formed in the Standard Big Bang Nucleosynthesis. We call such dark atoms Ohelium (OHe) [17] and assume that they are the dominant form of the modern dark matter. Here we concentrate on effects of O-helium dark matter in underground detectors. We present qualitative confirmation of the earlier guess [17, 18, 19, 20] that the positive results of dark matter searches in DAMA/NaI (see for review [21]) and DAMA/LIBRA [22] experiments can be explained by O-helium, resolving the controversy between these results and the results of other experimental groups. X −− ,

2 2.1

Radiative capture of OHe in the underground detectors O-helium in the terrestrial matter

The evident consequence of the O-helium dark matter is its inevitable presence in the terrestrial matter, which appears opaque to O-helium and stores all its in-falling flux. After they fall down terrestrial surface, the in-falling OHe particles are effectively slowed down due to elastic collisions with matter. Then they drift, sinking down towards the center of the Earth with velocity V =

g ≈ 80S3 A1/2 cm/ s. nσv

(1)

Here A ∼ 30 is the average atomic weight in terrestrial surface matter, n = 2.4 · 1024 /A cm−3 is the number density of terrestrial atomic nuclei, σv is the rate of nuclear collisions, mo ≈ MX + 4mp = S3 TeV is the mass of O-helium, MX is the mass of the X −− component of O-helium, mp is the mass of proton and g = 980 cm/ s2 . Near the Earth’s surface, the O-helium abundance is determined by the equilibrium between the in-falling and down-drifting fluxes. The in-falling O-helium flux from dark matter halo is F =

n0 · |Vh + VE |, 8π

where Vh -speed of Solar System (220 km/s), VE -speed of Earth (29.5 km/s) and n0 = 3·10−4 S3−1 cm−3 is the local density of O-helium dark matter. For qualitative estimation we don’t take into account here velocity dispersion and distribution of particles in the incoming flux that can lead to significant effect. 2

At a depth L below the Earth’s surface, the drift timescale is tdr ∼ L/V , where V ∼ 400S3 cm/ s is given by Eq. (1). It means that the change of the incoming flux, caused by the motion of the Earth along its orbit, should lead at the depth L ∼ 105 cm to the corresponding change in the equilibrium underground concentration of OHe on the timescale tdr ≈ 2.5 · 102 S3−1 s. The equilibrium concentration, which is established in the matter of underground detectors at this timescale, is given by noE =

2π · F nσv = n0 · |Vh + VE |, V 4g

(2)

where, with account for Vh > VE , relative velocity can be expressed as q q |Vo | = (Vh + VE )2 = Vh2 + VE2 + Vh VE sin(θ) ≃ ≃ Vh

r

1+

1 VE VE sin(θ) ∼ Vh (1 + sin(θ)). Vh 2 Vh

Here θ = ω(t − t0 ) with ω = 2π/T , T = 1yr and t0 is the phase. Then the concentration takes the form (1)

(2)

noE = noE + noE · sin(ω(t − t0 ))

(3)

So, there are two parts of the signal: constant and annual modulation, as it is expected in the strategy of dark matter search in DAMA experiment [22].

2.2

Radiative capture of O-helium by sodium

In the essence, our explanation of the results of experiments DAMA/NaI and DAMA/LIBRA is based on the idea that OHe, slowed down in the terrestrial matter and present in the matter of DAMA detectors, can form a few keV bound state with sodium nuclei, in which OHe is situated beyond the nucleus. Radiative capture to this bound state leads to the corresponding energy release and ionization signal, detected in DAMA experiments. The rate of radiative capture of OHe by nuclei can be calculated [19, 20] with the use of the analogy with the radiative capture of neutron by proton with the account for: i) absence of M1 transition that follows from conservation of orbital momentum and ii) suppression of E1 transition in the case of OHe. Since OHe is isoscalar, isovector E1 transition can take place in OHe-nucleus system only due to effect of isospin nonconservation, which can be measured by the factor f = (mn − mp )/mN ≈ 1.4 · 10−3 , corresponding to the difference of mass of neutron,mn , and proton,mp , relative to the mass of nucleon, mN . In the result the rate of OHe radiative 3

capture by nucleus with atomic number A and charge Z to the energy level E in the medium with temperature T is given by σv =

f πα 3 Z 2 T √ ( ) p . 2 mp 2 A Amp E

(4)

Formation of OHe-nucleus bound system leads to energy release of its binding energy, detected as ionization signal. In the context of our approach the existence of annual modulations of this signal in the range 2-6 keV and absence of such effect at energies above 6 keV means that binding energy of Na-OHe system in DAMA experiment should not exceed 6 keV, being in the range 2-4 keV. The amplitude of annual modulation of ionization signal (measured in counts per day per kg, cpd/kg) is given by 3πα · no NA VE tQ f Zi T T f Zi ( )2 p = ai 2 ( )2 p . √ 1/2 2 A S m A S A A m E i i p i i mp Ei 640 2Amed (AI + AN a ) 3 p i 3 (5) Here NA is Avogadro number, i denotes Na, for which numerical factor ai = 4.3 · 1010 , Q = 103 (corresponding to 1kg of the matter of detector), t = 86400 s, Ei is the binding energy of Na-OHe system and n0 = 3 · 10−4 S3−1 cm−3 is the local density of O-helium dark matter near the Earth. The value of ζ should be compared with the integrated over energy bins signals in DAMA/NaI and DAMA/LIBRA experiments and the result of these experiments can be reproduced for EN a = 3 keV. The account for energy resolution in DAMA experiments [23] can explain the observed energy distribution of the signal from monochromatic photon (with EN a = 3 keV) emitted in OHe radiative capture. At the corresponding values of µ and g2 there is no binding of OHe with iodine and thallium [1]. It should be noted that the results of DAMA experiment exhibit also absence of annual modulations at the energy of MeV-tens MeV. Energy release in this range should take place, if OHe-nucleus system comes to the deep level inside the nucleus. This transition implies tunneling through dipole Coulomb barrier and is suppressed below the experimental limits.

ζ=

2.3

OHe radiative capture by other nuclei

For the chosen range of nuclear parameters, reproducing the results of DAMA/NaI and DAMA/LIBRA, our results [1] indicate that there are no levels in the OHe-nucleus systems for heavy nuclei. In particular, there are no such levels in Xe and most probably in Ge, what seem to prevent direct comparison with DAMA results in CDMS and XENON100 experiments. However, even in this case presence of silicon in the chemical composition 4

of CDMS set-up can provide some possibility for test of OHe interpretation of these results. The levels in Si-OHe system were calculated in [1]. The two sets of solutions were obtained for each of approximation in description of Yukawa potential: i the case (m) for nuclear Yukawa potential U3m , averaged over the orbit of He in OHe, ii the case (b) of the nuclear Yukawa potential U3b with the position of He most close to the nucleus. These two approximations correspond to the larger and smaller distance effects of nuclear force, respectively, so that the true picture should be between these two extremes. For the parameters, reproducing results of DAMA experiment the predicted energy level of OHe-silicon bound state is generally beyond the range 2-6 keV, being in the most cases in the range of 30-40 keV or 90-110 keV by absolute value. It makes elusive a possibility to test DAMA results by search for ionization signal in the same range 2-6 keV in other set-ups with content that differs from Na and I. Even in the extreme case (m) of ionization signal in the range 2-6 keV our approach naturally predicts its suppression in accordance with the results of CDMS [24]. It should be noted that strong sensitivity of the existence of the OHe-Ge bound state to the values of numerical factors [1] doesn’t exclude such state for some window of nuclear physics parameters. The corresponding binding energy would be about 450-460 keV, what proves the above statement even in that case. Since OHe capture rate is proportional to the temperature, it looks like it is suppressed in cryogenic detectors by a factor of order 10−4 . However, for the size of cryogenic devices less, than few tens meters, OHe gas in them has the thermal velocity of the surrounding matter and the suppression relative to room temperature is only ∼ mA /mo . Then the rate of OHe radiative capture in cryogenic detectors is given by Eq.(4), in which room temperature T is multiplied by factor mA /mo , and the ionization signal (measured in counts per day per kg, cpd/kg) is given by Eq.(5) with the same correction for T supplemented by additional factors 2Vh /VE and (AI + AN a )/Ai , where i denotes Si. To illustrate possible effects of OHe in various cryogenic detectors we give in Tables 1 and 2 energy release, radiative capture rate and counts per day per kg for the pure silicon for the preferred values of nuclear parameters.

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Table 1: Effects of OHe in pure silicon cryogenic detector in the case m for nuclear Yukawa potential U3m , averaged over the orbit of He in OHe [1]. g2 /µ2 , GeV −1 Energy, keV σV · 10−33 , cm3 /s ξ · 10−2 , cpd/kg

242 2.7 19.3 10.8

242 31.9 5.6 3.1

257 3.0 18.3 10.2

257 33.2 5.5 3.1

395 6.1 12.8 7.2

395 41.9 4.9 2.7

Table 2: Effects of OHe in pure silicon cryogenic detector for the case of the nuclear Yukawa potential U3b with the position of He most close to the nucleus [1]. g2 /µ2 , GeV −1 Energy, keV σV · 10−33 , cm3 /s ξ · 10−2 , cpd/kg

3

242 29.8 5.8 3.3

242 89.7 3.3 1.9

257 31.2 5.7 3.2

257 92.0 3.3 1.9

395 42.0 4.9 2.7

395 110.0 3.0 1.7

Conclusions

The results of dark matter search in experiments DAMA/NaI and DAMA/LIBRA can be explained in the framework of our scenario without contradiction with the results of other groups. This scenario can be realized in different frameworks, in particular, in the extensions of Standard Model, based on the approach of almost commutative geometry, in the model of stable quarks of 4th generation that can be naturally embedded in the heterotic superstring phenomenology, in the models of stable technileptons and/or techniquarks, following from Minimal Walking Technicolor model or in the approach unifying spin and charges. Our approach contains distinct features, by which the present explanation can be distinguished from other recent approaches to this problem [25] (see also for review and more references in [26]). The proposed explanation is based on the mechanism of low energy binding of OHe with nuclei. Within the uncertainty of nuclear physics parameters there exists a range at which OHe binding energy with sodium is in the interval 2-4 keV. Radiative capture of OHe to this bound state leads to the corresponding energy release observed as an ionization signal in DAMA detector. OHe concentration in the matter of underground detectors is determined by the equilibrium between the incoming cosmic flux of OHe and diffusion towards the center of Earth. It is rapidly adjusted and follows the

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change in this flux with the relaxation time of few minutes. Therefore the rate of radiative capture of OHe should experience annual modulations reflected in annual modulations of the ionization signal from these reactions. An inevitable consequence of the proposed explanation is appearance in the matter of DAMA/NaI or DAMA/LIBRA detector anomalous superheavy isotopes of sodium, having the mass roughly by mo larger, than ordinary isotopes of these elements. If the atoms of these anomalous isotopes are not completely ionized, their mobility is determined by atomic cross sections and becomes about 9 orders of magnitude smaller, than for O-helium. It provides their conservation in the matter of detector. Therefore mass-spectroscopic analysis of this matter can provide additional test for the O-helium nature of DAMA signal. Methods of such analysis should take into account the fragile nature of OHe-Na bound states, since their binding energy is only few keV. With the account for high sensitivity of the numerical results to the values of nuclear parameters and for the approximations, made in the calculations, the presented results can be considered only as an illustration of the possibility to explain puzzles of dark matter search in the framework of composite dark matter scenario. An interesting feature of this explanation is a conclusion that the ionization signal expected in detectors with the content, different from NaI, should be dominantly in the energy range beyond 2-6 keV. Moreover, it is shown that in detectors, containing light nuclei (e.g. helium-3) and heavy nuclei (e.g. xenon) there should be no bound states with OHe. In the framework of our approach it means that the physical nature of effects, observed in DAMA/NaI and DAMA/LIBRA experiments, cannot be probed in XENON10, XENON100 experiments or in the future detectors with He-3 content. Test of the nature of these results in CDMS experiment should take into account the difference in energy release and rate of radiative capture of OHe by silicon as well as in Ge, if OHe-Ge bound state does exist. The uncertainty in the existence of OHe-Ge bound state makes problematic direct test of our model in pure germanium detectors. It should be noted that the excess of low energy events reported in the CoGent experiment can be hardly explained by radiative capture of OHe. Therefore test of results of DAMA/NaI and DAMA/LIBRA experiments by other experimental groups can become a very nontrivial task. It is interesting to note that in the framework of our approach positive result of experimental search for WIMPs by effect of their nuclear recoil would be a signature for a multicomponent nature of dark matter. Such OHe+WIMPs multicomponent dark matter scenarios that naturally follow from AC model [12] and from models of Walking technicolor [18] can be also realized as OHe (dominant)+5th neutrino (sub-dominant) model in 7

the framework of spin-charge-family-theory [15] (see [16]). The presented approach sheds new light on the physical nature of dark matter. Specific properties of dark atoms and their constituents are challenging for the experimental search. The development of quantitative description of OHe interaction with matter confronted with the experimental data will provide the complete test of the composite dark matter model.

References [1] M. Y. Khlopov, A. G. Mayorov and E. Y. Soldatov, “Dark Atoms of the Universe: towards OHe nuclear physics” This Volume [2] M.Yu. Khlopov Cosmoparticle physics (World Scientific, Singapore, 1999). [3] M.Yu. Khlopov in Cosmion-94, Eds. M.Yu.Khlopov et al. (Editions frontieres, 1996) P. 67; M. Y. Khlopov in hep-ph/0612250 , p 51. [4] M. Y. Khlopov in arXiv:0711.4681, p. 114; M. Y. Khlopov and N. S. Mankoc-Borstnik, ibid, p. 195. [5] S. L. Glashow, arXiv:hep-ph/0504287. [6] D. Fargion and M. Khlopov, arXiv:hep-ph/0507087. [7] M.Yu. Khlopov, JETP Lett. 83, 1 (2006). [8] K. Belotsky et al, arXiv:astro-ph/0602261. K. Belotsky et al, Gravitation and Cosmology 12, 1 (2006); K. Belotsky et al, arXiv:0806.1067 [astro-ph]. [9] M. Y. Khlopov, arXiv:astro-ph/0607048. [10] K.M.Belotsky et al, Gravitation and Cosmology 11, 3 (2005) [11] C. A. Stephan, arXiv:hep-th/0509213. [12] D. Fargion et al, Class. Quantum Grav. 23, 7305 (2006); M. Y. Khlopov and C. A. Stephan, arXiv:astro-ph/0603187. M. Y. Khlopov and C. A. Stephan, arXiv:astro-ph/0603187. [13] M. Y. Khlopov and C. Kouvaris, Phys. Rev. D 77, 065002 (2008). [14] M. Y. Khlopov, arXiv:0801.0167 [astro-ph]; arXiv:0801.0169 [astro-ph].

8

M. Y. Khlopov,

[15] N.S. Mankoˇc Borˇstnik, This Volume; A. Borˇstnik Braˇciˇc, N.S. Mankoˇc Borˇstnik, Phys. Rev. D 74, 073013 (2006); N.S. Mankoˇc Borˇstnik, Mod. Phys. Lett. A 10, 587 (1995); N.S. Mankoˇc Borˇstnik, Int. J. Theor. Phys. 40, 315 (2001); G. Bregar, M. Breskvar, D. Lukman, N.S. Mankoˇc Borˇstnik, New J. of Phys. 10, 093002 (2008). [16] M. Y. Khlopov and N.S. Mankoˇc Borˇstnik, ”Can the stable fifth family of the ”spin-charge-family-theory” proposed by N.S. Mankoˇc Borˇstnik fulfil the M.Y. Khlopov requirements and form the fifth antibaryon clusters with ordinary He nucleus?” This Volume [17] M. Y. Khlopov, arXiv:0806.3581 [astro-ph]. [18] M. Y. Khlopov and C. Kouvaris, Phys. Rev. D 78, 065040 (2008) [19] M. Y. Khlopov, A. G. Mayorov and E. Y. Soldatov, Int. J. Mod. Phys. D 19 (2010) 1385 [arXiv:1003.1144 [astro-ph.CO]]. [20] M. Y. Khlopov, AIP Conf. Proc. 1241 (2010) 388 [arXiv:0911.5685 [astro-ph.CO]]. [21] R. Bernabei et al., Rivista Nuovo Cimento 26, 1 (2003) [22] R. Bernabei et al. [DAMA Collaboration],Eur.Phys.J C56, 333 (2008) arXiv:0804.2741 [astro-ph]. [23] R. Bernabei et al. [DAMA Collaboration], Nucl. Instrum. Meth. A 592 (2008) 297 [arXiv:0804.2738 [astro-ph]]. [24] O. Kamaev, for the CDMS Collaboration, arXiv:0910.3005 [hep-ex]. [25] F. Petriello and K. M. Zurek, JHEP 0809, 047 (2008); R. Foot, Phys. Rev. D 78, 043529 (2008); J. L. Feng, J. Kumar and L. E. Strigari, arXiv:0806.3746 [hep-ph]; J. L. Feng, J. Kumar, J. Learned and L. E. Strigari, arXiv:0808.4151 [hep-ph]; E. M. Drobyshevski, arXiv:0811.0151 [astro-ph]; B. Feldstein, A. L. Fitzpatrick and E. Katz, JCAP 1001 (2010) 020 [arXiv:0908.2991 [hep-ph]]; B. Feldstein, A. L. Fitzpatrick, E. Katz and B. Tweedie, JCAP 1003 (2010) 029 [arXiv:0910.0007 [hep-ph]]; A. L. Fitzpatrick, D. Hooper and K. M. Zurek, Phys. Rev. D 81 (2010) 115005 [arXiv:1003.0014 [hepph]]; S. Andreas, C. Arina, T. Hambye, F. S. Ling and M. H. G. Tytgat, Phys. Rev. D 82 (2010) 043522 [arXiv:1003.2595 [hep-ph]]; D. S. M. Alves, S. R. Behbahani, P. Schuster and J. G. Wacker, JHEP 1006 (2010) 113 [arXiv:1003.4729 [hep-ph]]; V. Barger, M. McCaskey and G. Shaughnessy, Phys. Rev. D 82 (2010) 035019 [arXiv:1005.3328 9

[hep-ph]]; C. Savage, G. Gelmini, P. Gondolo and K. Freese, arXiv:1006.0972 [astro-ph.CO]; D. Hooper, J. I. Collar, J. Hall and D. McKinsey, arXiv:1007.1005 [hep-ph]; S. Chang, R. F. Lang and N. Weiner, arXiv:1007.2688 [hep-ph]; S. Chang, N. Weiner and I. Yavin, arXiv:1007.4200 [hep-ph]; V. Barger, W. Y. Keung and D. Marfatia, arXiv:1007.4345 [hep-ph]. A. L. Fitzpatrick and K. M. Zurek, arXiv:1007.5325 [hep-ph]; T. Banks, J. F. Fortin and S. Thomas, arXiv:1007.5515 [hep-ph]; B. Feldstein, P. W. Graham and S. Rajendran, arXiv:1008.1988 [hep-ph]. [26] G. B. Gelmini, Int. J. Mod. Phys. A 23 (2008) 4273 [arXiv:0810.3733 [hep-ph]]; J. L. Feng, arXiv:1003.0904 [astro-ph.CO].

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